The episode is a Bottle Show - a term for an episode designed to keep costs low by using pre-existing sets, minimal effects and the like. This allows for other episodes to go to town. In this case The Drumhead saved $250,000 for other episodes to use. (For reference, during discussions of Babylon 5's budget, JMS claimed TNG ran about a million per episode)
The original plan was for the episode to refer to incidents Admiral Satie would bring up with clips from the episodes in question, but Rick Berman and Michael Piller objected as they didn't want to draw parallels with Shades of Grey.
The episode was written by Jeri Taylor, but the concept came from a Ron Moore concept for an episode titled "It Can't Happen Here", which would refer to the McCarthy trials and the Salem Witch Hunts. Moore would revisit the concept in Battlestar Galactica, in the first series episode Litmus. But more on that later.
Jonathan Frakes directed the episode, and specifically visually referenced courtroom dramas including The Caine Mutiny, and Judgement at Nuremberg (which starred William Shatner).
The events referenced during the episode come from Conspiracy, Sins of the Father, The Best of Both Worlds I and II, Family, and Data's Day. It's also the first episode to note the number of ships and people lost at Wolf 359.
The set for the Interrogation room was first seen in The Defector, and is a redress of the Enterprise Bridge from the first three Trek movies.
Simon Tarses would become a recurring character in the later DS9 novels, having either been exonerated or rebuilding his career. He served as a doctor on the station, later transferring to USS Aventine under Captain Ezri Dax,
Jeri Taylor, Michael Dorn and Jonathan Frakes all cited this as a favourite episode, Frakes specifically said he enjoyed the chance to work with Jean Simmons.
And onto the episode:
When @Mike first brought this episode up it was in relation to The Measure of A Man, and interestingly my memory of the episode is that the inquiry scenes were much longer, just like I remembered the court scenes took more space in Measure of a Man. The two episodes are quite similar structurally, in that the problem is set up, a bunch of conversations about the problem happen, and then there's a speech in court that resolves the problem. But as glib as I make it sound there, it's a really good episode.
One thing that works quite well is that Worf buys into Satie's rhetoric, going so far as to direct Enterprise security staff to investigate Tarses to a very intrusive level. It sets up a simmering conflict between Picard and Worf, especially as Picard basically spends the middle of the episode making vague proclamations about totalitarianism and paranoid witch hunts, which we understand the context of, but you can easily interpret as Picard getting paranoid himself if you were the recipient of said speeches. I don't know if that was intentional, but it stuck me as quite amusing this time through the ep.
In Satie's defence, the reference to Conspiracy shows what she's been doing for years - rooting out the brain slugs (or if you've read the DS9 novels, the evil Trill symbiont offshoots) that tried to take over the Federation, and it's understandable that she would see traitors where there aren't any, especially if Picard had been assimilated by the Borg and used to almost take over Earth only a few months earlier. The parallels between the brain slugs and the Borg are quite subtle and again, not sure if they're there on purpose, but cool.
Overall, I think the episode's flaw is quite similar to one of Measure of a Man's, in that the problem is solved by Picard giving a speech that in this case causes Satie to lose her shit and all of a sudden nobody takes her seriously any more. It's incredibly pat and a limitation of the encapsulated format of TV storytelling at the time. To bring Litmus from BSG back into the post, it's interesting to compare the conclusions of the episodes - Picard gives a speech, Adama walks out on the inquiry and refuses to allow it access to his ship any more - but in BSG it causes knock-on effects, in Adama and Roslin's rivalry for example.
The episode's power is that it shows how easy it is to fall into the trap of extremism. J'Dan says the blood of all Klingons has become like water. Satie was raised from childhood to make sure the Federation was preserved. They both take steps that go against their culture - siding with the Romulans in J'Dan's case, or hounding people for minor infractions and trumped up charges in Satie's. The title of Moore's concept that lead to the episode - It Can't Happen Here - has a cultural weight to it, and ties directly into the idea that the Federation shouldn't be the site of a witch hunt. It's a concept DS9 would explore a lot as well, notably with Section 31 and Admiral Layton's coup in Homefront/Paradise Lost.